feat(timeline): derive header meta figures from the DTO (REQ-002)

A pure timelineMeta() returns the year range (first/last band, null when
there are no bands) and the letter/event totals across all year bands plus
the undated bucket — the single place these counts are computed.

Refs #833
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

frontend/src/lib/timeline/timelineMeta.ts

@@ -0,0 +1,31 @@
+import type { components } from '$lib/generated/api';
+
+type TimelineDTO = components['schemas']['TimelineDTO'];
+
+export interface TimelineMeta {
+	/** First year band's year, or `null` when there are no bands. */
+	firstYear: number | null;
+	/** Last year band's year, or `null` when there are no bands. */
+	lastYear: number | null;
+	/** Every `LETTER` entry across all year bands plus the undated bucket. */
+	letterCount: number;
+	/** Every `EVENT` entry (derived, curated, and historical) across all bands plus undated. */
+	eventCount: number;
+}
+
+/**
+ * Derives the header meta-line figures from a loaded `TimelineDTO` (REQ-002):
+ * the year range (first/last band) and the letter/event totals across every
+ * year band plus the undated bucket. Pure and the single place these counts
+ * live — the route renders them; `TimelineView` never recomputes them.
+ */
+export function timelineMeta(timeline: TimelineDTO): TimelineMeta {
+	const years = timeline.years;
+	const allEntries = [...years.flatMap((y) => y.entries), ...timeline.undated];
+	return {
+		firstYear: years.length ? years[0].year : null,
+		lastYear: years.length ? years[years.length - 1].year : null,
+		letterCount: allEntries.filter((e) => e.kind === 'LETTER').length,
+		eventCount: allEntries.filter((e) => e.kind === 'EVENT').length
+	};
+}